Parameter Workbench
Simulated Controls
6
6
0.45
0.05
0.32
Canonical Forensic Analysis
Coin Cluster
Identified Fallacy
Gambler's Fallacy & Clustering Illusion
Observed P-Value
0.32
Inflated Alpha (αtrue)
0.19
P(Next Outcome is H)
0.500
Audit Trail & Reproducible Report
JSON state payload prepared with verified mathematical deltas
Biostatistical Grounding & Expert Pitfalls
Statistical intuition frequently fails even seasoned researchers when interpreting sequences, significance thresholds, and repeated measures. Based on biostatistical findings and probability axioms, this laboratory exposes three critical vulnerabilities:
1. Gambler's Fallacy & Clustering Illusion
Observing 6 heads in a row with a fair coin has an exact prior probability of (1/2)6 = 0.0156. Yet conditionally, the 7th toss remains strictly independent at P(H) = 0.500. Brains mistake random cluster anomalies for broken independence or assume a compensatory "reversion" is owed.
2. High P-Value ≠ Proof of the Null Hypothesis
A non-significant test statistic (e.g. p = 0.32) simply indicates the observed deviation is consistent with chance variation under H0. It does not prove the effect size is zero or that normality assumptions hold. Absence of evidence is not evidence of absence.
3. Autocorrelation & Massive Type-I Error Inflation
Standard regression and t-tests assume independent and identically distributed errors. When repeated measurements exhibit positive serial autocorrelation (ρ > 0), the effective sample size collapses and nominal α = 0.05 inflates dramatically (reaching 0.19 to 0.25+), causing false-positive scientific discoveries.